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What color hat am I wearing?   ...   random thoughts , logic , math
tue 2005-may-10 15:07:22 pdt   ...   permalink

The 2-player game

Two players sit facing each other, each with a red or blue hat placed on her head; each can see the other's hat but not her own. Each player must write down a guess, "red" or "blue", for her own hat color, without knowing the other player's guess. The guesses are then revealed and:

  • if at least one player is correct, both get a million dollars;
  • if both are wrong, they get nothing.
  • They can of course agree on their strategy ahead of time but cannot communicate once the game begins. Obviously if they both just guess randomly, they win with 3/4 probability. But can you come up with a strategy that has a better chance of winning? Can you guarantee a win?

    Yes, you can guarantee a win.

    (a hint for how)

    Please do NOT post solutions in the comments below. Thanks.

    mail me

    post a comment on this entry

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